The Morse-Novikov Number of a Knot

The projection map of the boundary of a knot complement to S1 to its
meridian (which is constant on the longitude) extends to a circle-valued Morse function on the complement.
The minimal number of critical points for such an extension is called the "Morse-Novikov number" of a knot,
MN(K). Clearly, MN(K) = 0 if and only if K is fibered. Since the Euler characteristic of the complement is
0, MN(K) is always even.

The Morse-Novikov number was introduced in a paper by Pajitnov, Rudolph, and Weber,
referenced below, in which estimates on its value are developed along with some computations.
Goda, in his paper on the subject, Some Estimates.., announced the computation of the value of
MN(K) for all prime knots of crossing number 10 or less. (The value is 2 for all such knots that are not
fibered.) This result was based on his earlier paper, On the handle number ... .